A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained tensorizing the Virtual Element (VE) discretization in space with the Discontinuous Galerkin (DG) method in time. As such, it combines the advantages of both the VE and the DG methods. The proposed scheme is implicit and it is proved to be unconditionally stable and accurate in space and time.

翻译：提出了一种新颖的时空离散化方法，用于(linear)标量耗散波动方程，也是一种结构化方法，即在空间离散化中采用虚拟元VE方法，同时采用不连续Galerkin（DG）方法对时间进行离散化。因此，它结合了VE和DG方法的优点。所提出的方案为隐式方案，并证明在空间和时间上无条件稳定和精确。